The PC Sound Card as a Voltage Measurement
Contents
1. Additionally the transformer used in the circuit behaves differently depending on the frequency of the signal passed through it The realistic behavior of the components in the preprocessing circuit will produce an effect on the overall frequency response of the system Work could also be done to make the calculation code more efficient to allow the computation of the a and bz values required by IEC standard 61000 4 7 Furthermore the final results of the experimental measurements must be independently verified before the voltage measurement platform can be used as a trusted DAQ Other applications can be approached as well Any process which requires voltage measurements to be processed by a computer can and should be attempted using this voltage measurement platform For each new application new code will have to be developed and the results independently verified by equipment which already exists for the desired purpose 39 1 2 3 4 5 6 7 8 9 References Claus Riethm ller Windows Driver API Basics ST Audio Knowledge Base lt http www staudio de kb english drivers gt January 2003 accessed June 2013 PortAudio PortAudio API Overview lt http portaudio com docs v19 doxydocs api_overview html gt accessed July 2013 Mark Heath Sound Code What s Up With WASAPI lt http mark dot net blogspot com 2008 06 what up with wasap1 html gt June 2008 accessed June2. 2 a gt YC Nxh N 2 T a T 7 C NXxA N 2 8 k N 2 1 The smoothing block in Figure 16 passes the results of the grouping block over time through a low pass filter This filtering removes any sudden disturbances from the grouped harmonic values over time and results in a smooth plot of harmonic values over time This smoothed output makes up Output 2b and is referred to as Y yn A diagram depicting the low pass filter used in the smoothing operation is shown in Figure 18 10 The a and values are prescribed by the IEC standard and are shown in Table 1 The z operation refers to a delay of one window width Output 2b is then further processed and compared with harmonic limits standards to determine if the measured voltage signal is in compliance Figure 18 Smoothing Filter Diagram Table 1 Smoothing Filter Values a 8012 Ap 702 22 Because these harmonic measurements are taken over an extended period of time the timing of the calculations is important The smallest unit of time relevant to these calculations is the 200 ms window width used by the DFT operation Furthermore the IEC standard dictates that the 200 ms values be averaged using the root mean square method every 3 s These 3 s values are then averaged using the same method every 10 min There are therefore new values every 200 ms 3 s and 10 min 5 2 Harmonic Calculations Equations 5 and 6 are in a continuous time domain form In order to imp
3. 2014 National Instruments NI Educational Laboratory Virtual Instrumentation Suite II Series NI ELVIS IT Series User Manual January 2009 Edward W Kamen and Bonnie S Heck Fundamentals of Signals and Systems Using the Web and MATLAB 3rd ed Pearson Education 2007 National Instruments Zero Padding Does Not Buy Spectral Resolution lt http www n1 com white paper 4880 en gt September 2006 accessed July 2013 Alan V Oppenheim and Ronald W Schafer Discrete Time Signal Processing 3rd ed Prentice Hall 2010 Victor P Nelson H Troy Nagle Bill D Carroll and J David Irwin Digital Logic Circuit Analysis and Design Prentice Hall 1995 John Hung and Victor Nelson Embedded Systems Design Lab Lecture Fall 2010 40 10 IEC Amendment to IEC 61000 4 7 Ed 2 Electromagnetic compatibility EMC Testing and measurement techniques General guide on harmonics and interharmonics measurements and instrumentation for power supply systems and equipment connected thereto March 2008 41
4. LINTU Hoisas EE E NA E l Chapter 2 Software Characterization id A 4 DAs DIVE e OCC OO UU On 4 ZAPOA Ud Oean T E T E aeA een 5 Chapter 3 Voltage Measurement PlatforM ooooocococconoccnoccccccnnnnnnnnnnnnnnnnnn os 9 Ao ALOWALC E E A E Se 9 IEPENE NaON LO ar E E neaceeeesees 10 9 POA udio CAI iaa 10 34 Sampin Rate Capabilities ti aw ei hatewitene eens aes 1 39 bale Let Coury at 1 36 Maenitude Frequency Response 12 Sl CONMMUILY est is is 13 Chapter 4 Signal Processing Principles 0 0 cece ccc cece eee eee e eee e eee e cece eee inia 17 4 1 Fourier Series and the Fourier Transform ccccceeeeeeeeeee eee ees 17 4 2 Discrete Fourier Transform Concerms ccc cece cece cece ee ccee eee eens 20 111 Aso ample Rate COn Ver OM tirada 25 Chapter 3 Sample APpliCAHON Na 28 A A A ue besatatans 28 32 Harmon Calcula eeri E EEE 33 TOL Pm RES e ia e des 35 Chapter o CORA ad se 38 A A SR RR 40 1V Table 1 Smoothing Filter Values List of Tables Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 List of Figures AMAN AID O ct 4 PortAudio and DT VETS escote artis 6 Input Voltasetto Output V aC erior s re NETON EEAO 12 Masmtuide RESPONSO iaa 13 W MMIE ona y Result osos An 15 Fourier Transform Exa AA A 19 DTT Exaile rap
5. analog values such as voltage into digital values Once converted these digital values can be used by computer systems to perform whatever calculations are necessary for the application It is possible however to remove the DAQ device from this process Because computers often must be used in conjunction with DAQ devices it is financially advantageous to implement the functionality of a DAQ device using hardware that already exists on a computer The hardware component that can be most readily applied to this problem is the sound card Sound cards are peripheral devices for computer systems that process audio information Audio information is sent to speakers or headphones to produce sound Also audio information can be recorded to a file when acquired from a mic This recording capability utilizes an ADC to measure AC voltage signals in exactly the same manner as a DAQ device Therefore software can be developed which replaces the traditional DAQ device with a sound card Sound cards come standard on the vast majority of personal computers and are therefore more economically advantageous than a DAQ device provided that certain minimum performance requirements are met Many of these requirements are specific to the application and cannot be addressed in a general discussion However there are some general requirements that can be addressed The sound card must be capable of continuous recording while the controlling software performs whatever
6. as shown in 2 in Chapter 4 The Yc y term is the RMS value of the coefficients in the single sine form of the Fourier series as shown in 1 in Chapter 4 The equations for calculating these quantities are shown in 5 6 and 7 10 In these equations Ty is the window width for the DFT operation in seconds w4 is the fundamental frequency of the measured signal in radians per second N is the number of fundamental periods in one window width and k is the spectral order 2 IN k Ay T f t cos ot dt 5 2 te k z 2 a 2 You EA 7 2 2 The grouping block in Figure 16 forms harmonic groups from the spectral components immediately surrounding the harmonic frequency components This operation is performed because of the frequency bleeding phenomenon If the spectral content of the measured signal does not fall precisely on the expected harmonic value then the energy at that harmonic frequency will bleed into the surrounding frequency bins in the DFT result In order to catch potentially bleeding energy the spectral components 31 surrounding the harmonic components are summed into harmonic groups These groups make up Output 2a and are passed to the next block for further processing The harmonic group quantities are referred to as Y n The equation used to calculate these quantities is shown in 8 10 In this equation the Y g terms are the results of equation 7 and h is the harmonic order i N 2 1 1
7. of the DirectX package which is most often used as the driver platform of choice for game developers since Windows 95 1 The DirectSound API is therefore available to all modern Windows computers However there is no guarantee that the DirectX package will have been installed on a given machine WASAPI was created as a replacement for WMME and has been standard on all Windows machines since Windows Vista 3 PortAudio accesses the audio card hardware using a software construct known as a stream Streams are specialized objects in an application s code which determine the size shape and type of data that is to be passed to or taken from the hardware There are many parameters that go into defining a stream A few of the more important parameters are the number of input output channels the format for the data being streamed and the length of the stream s buffer 2 A PortAudio stream can be set up to take input and provide output simultaneously Alternatively a stream can be purely input or purely output The number of data channels that can be opened in either direction is dependent on hardware The data format parameter for PortAudio streams can be 32 bit floating point 32 bit 24 bit 16 bit and 8 bit integer as well as 8 bit unsigned integer The values available for each of the integer data formats are merely the range of values inherent to that data type In the case of the 8 bit unsigned integer format a value of 128 is co
8. operate on discrete time signals However because the result is still a continuous signal it cannot be computed by a digital device To solve this issue the discrete Fourier transform DFT is used The DFT takes a discrete time domain signal and generates a discrete frequency domain signal All signals involved are discrete in nature therefore the results of this transform can be accurately calculated 19 using a computer As is shown in Figure 8 the periodicity of the continuous DTFT results is still present in the discrete DFT results It is helpful to think of the DFT results as being a sampled version of the DTFT results DFT Input DFT Output X f IDFT x n l 0 Time ms Frequency kHz Figure 8 DFT Example The DFT is completely calculable by a computer However completing the full calculation is computationally intensive The periodic and symmetric nature of the result can be exploited to simplify the calculations involved When this approach is taken the resulting algorithm is called a fast Fourier transform FFT It is important to note that the total number of points operated on using most FFT algorithms must be a power of two Other than this limitation on the size of the input sequence use of an FFT algorithm does not affect the frequency domain result Mathematically FFT algorithms are identical to the DFT they are just less computationally intensive 4 2 Discrete Fourier Transform Concerns There
9. use as a voltage measurement platform it is necessary that an application should first be able to record data coming into the sound card Beyond that certain electrical and operational characteristics must be known about the device These characteristics include such things as transfer characteristics frequency response and whether or not the hardware can take measurements continuously 3 1 Hardware The PC soundcard used for this experiment was integrated on the motherboard of a Dell Studio SPX laptop manufactured in 2009 As such the electrical specifications for the sound card were not available for reference This fact meant that all pertinent specifications had to be acquired through experimentation The electrical characteristics that were determined experimentally include available sampling frequencies input voltage to output value transfer curve and magnitude frequency response The specific hardware component on the sound card that was tested was the mic input jack This port accepts a standard one eighth inch audio cable or TRS cable A TRS cable has three contacts a ground or reference line and two separate signal channels The mic input works on measuring a voltage signal using an ADC Using this hardware for measurement provides two input channels for voltage signals 3 2 Experimentation Tools In order to determine the electrical characteristics of the mic input jack a signal generator was required The signal generator
10. Fourier transform of a continuous time domain signal x t produces a continuous frequency domain signal FT x t with content up to the maximum frequency fmax of the original signal A representation of FT x t is shown in Figure 9 Now assume that x t is sampled at the Nyquist rate to generate the discrete time signal x n The DTFT of this new signal DT FT x n would not overlap as is shown in Figure 10 However if x t were to be sampled below the Nyquist rate to produce the signal x n overlapping would occur between the spectral copies in the DTFT results DT FT x n This overlapping is shown in Figure 11 Because the results of the DFT are merely a sampled version of the results of the DTFT this example 1s also applicable to the DFT and therefore FFT algorithms 22 FT x t oe Figure 9 Fourier Transform Frequency Envelope DTFT x n 0 TN Figure 10 Transformed Signal Sampled at the Nyquist Rate DTFT x n ON E Figure 11 Transformed Signal Sampled at Below the Nyquist Rate Aliasing has the effect of corrupting frequency components in the base copy of the signal spectrum with the addition of higher frequencies from adjacent spectral copies that are beyond the maximum frequency that can be represented by the FFT operation Often it is impossible to determine beforehand what the maximum frequency content of a signal will be In such cases in order to prevent aliasing the continuo
11. The PC Sound Card as a Voltage Measurement Platform in Power System Applications by Joel Allen Killingsworth A thesis submitted to the Graduate Faculty of Auburn University in partial fulfillment of the requirements for the Degree of Master of Science Auburn Alabama December 13 2014 Keywords Sound Card Voltage Measurement Voltage Harmonic Measurement IEC 61000 4 7 Copyright 2014 by Joel Allen Killingsworth Approved by S Mark Halpin Chair Professor of Electrical and Computer Engineering Charles A Gross Professor Emeritus of Electrical and Computer Engineering Thaddeus Roppel Professor of Electrical and Computer Engineering Abstract In this thesis document the feasibility of using a PC sound card to replace traditional data acquisition DAQ devices for the measurement of voltage signals in power system applications is discussed Communication between software applications and sound card hardware is established through the use of the PortAudio software library for audio applications A PC sound card is tested using the example application of voltage harmonic measurement structured to be consistent with the requirements found in IEC standard 61000 4 7 It is found that a PC sound card is capable of continuous recording under the load of heavy calculation and signal processing for an indefinite period of time 11 Table of Contents OSMA road 11 MAA o T S TT V WSU AN Na vi Listo ADO VAGON Seg O E viii C haper
12. approximately 135 mV It is clear from Figure 3 that the tested sound card has a built in gain of approximately 7 25 vi Voltage Recording Transfer Curve dE nu T a eee TAS LEER ete tae Sets ee o D ies A x 3 a NOL AA ia ci PEIE AS e Me A a A P 3 r z O hl ee is A PR E IIET asin s E Mb dsc A AS gt parese cs A ada EAS oO A 3 E k s 05 LANA DERE enidan eie ROIN ra RA AAA DANA D 7 ga z 5 2 A pres a TE a Beceren Pesii PARR we OB peee OSES EA TRIAS ESRUS INTE IO D A E SOD perenes ENANA RARO Ps re AS D or Cit kn ERA PAS RAN SA AR AS 0 a A F 0 20 40 60 80 100 120 140 Input Voltage Amplitude mV Figure 3 Input Voltage to Output Value 3 6 Magnitude Frequency Response The next step in the characterization of the sound card mic input jack was to find the frequency response Frequency response characterization is accomplished by passing a set of input signals through a system recording the output and comparing the two This comparison is performed by way of the Fourier transform and results in both a magnitude versus frequency curve and a phase versus frequency curve Only the magnitude portion of the frequency response was considered in this experiment It 1s important to note that the phase response would also be useful information Howev
13. are some practical concerns that must be addressed regarding the use of an FFT algorithm to analyze the frequency content of a signal First there is the concept of frequency resolution Because the FFT produces a discrete frequency domain signal 20 there must be some distance in the frequency spectrum between consecutive points in the calculation result The closer these points are together in the frequency spectrum the greater the frequency resolution Frequency resolution is determined by the sampling frequency of the discrete time domain signal and the total number of points being used 6 This relationship is shown in 3 where fg is the spacing between points fs is the sampling frequency used to sample the discrete time domain signal from the original continuous time domain signal and M is the total number of points being used _ 4s 3 7 3 fe Inspection of the relationship in 3 reveals that the spacing between points is the inverse of the length of time represented by the time domain samples being used or window width Ty This relationship is demonstrated in 4 where T is the sampling period and is the inverse of fg Frequency resolution is therefore directly controlled by the length of time that is used as input for the FFT operation 1 1 M MT Ty fe This spacing between points in the frequency domain result can cause problems if some of the frequency content of the time domain signal does not fall exa
14. calculations are required in real time In addition this continuous operation must be sustainable for an indefinite period of time In order to determine 1f these requirements are achievable using a PC sound card it is necessary to perform tests on specific software and hardware components Communication with the hardware must be established followed by determining the electrical characteristics of the recording device on the sound card Finally processing and recording experimental data is necessary to determine the fitness of the sound card for use as a voltage measurement platform Chapter 2 Software Characterization In order to use a PC sound card for voltage measurements it 1s first necessary to understand how to communicate with the sound card hardware In a Windows operating system environment peripheral hardware components such as sound cards are controlled through software packages known as drivers Applications developed by programmers can interface with these drivers in order to communicate with the hardware they control 2 1 Drivers Drivers are made up of two layers There 1s the layer which communicates directly with the sound card This layer is known as the driver kernel The second layer communicates with a program This layer is known as the driver application programming interface API 1 This hierarchy is shown in Figure 1 Application API 1 API 2 API 3 Sound Card Hardware Figure 1 Anatomy o
15. ctly where a point is defined to represent it For example if a signal has energy at 8 Hz and an FFT is performed on the signal with 5 Hz between each resulting point the result would have information available at 5 Hz and 10 Hz but not at 8 Hz The FFT would spread the 8 Hz energy to the surrounding available points Itis helpful to think of each point as a bin in which a range of possible frequencies collect In this example some of the 8 Hz 21 energy would show up in the 5 Hz bin and the 10 Hz bin or even beyond This phenomenon is known as frequency bleeding 6 It is therefore necessary to make sure that all frequencies of interest in a given time domain signal will fall neatly into a frequency bin and will not be left to bleed out over several bins Another issue brought about by the fact that the FFT operation 1s completely calculable is that the results of the FFT do not extend to infinite frequency There is a maximum frequency that can be represented by a given FFT operation This maximum frequency is equal to fs 2 6 Because the FFT results are periodic as is shown in Figure 8 if the time domain signal were to contain energy at frequencies higher than fs 2 the spectral copies would begin to overlap This overlapping is called aliasing 7 The minimum sampling rate to prevent aliasing is twice the highest frequency component of the signal to be sampled This minimum rate is known as the Nyquist rate 7 For example the
16. e lengthy process of writing data to a file The typical solution for this issue is to increase the length of the buffer so that there is more time in between buffers to record the data to a file This solution also increases the time needed to perform calculations but not nearly as much as it increases the available time Upon examination of the data file recorded for the WMME continuity test 1t was clear that some data had indeed been skipped As previously mentioned WMME 14 performs sample rate conversion automatically The time delay between signal input and recorded data point or latency 1s therefore relatively high This high latency can result in periodically dropping values in order to catch back up with the real time input The spikes in the derivative data are shown in Figure 5 These spikes were identified by finding data points with an absolute value greater than approximately 0 723 as dictated by the 0 2 V peak to peak input along with the gain of 7 25 Vv depicted in Figure 3 alu ha soundcard float y Figure 5 WMME Continuity Results The second continuity test was run using WASAPI to access the mic input jack The test signal was the same as before The only difference was that the hardware was sampling at 44 1 kHz Once the signal was sampled linear interpolation was used to achieve a virtual sampling rate of 7 68 kHz the same rate as the previous test The derivative operation was then
17. encies In order to properly handle the measurement of these signals and any associated calculations it 1s important to understand a few concepts in the field of digital signal processing When it comes to measurement and instrumentation digital signal processing is a field of great importance The ability to use computers to process data rather than relying on analog components provides a large degree of flexibility Designs can be altered on the fly by simply changing a line of code whereas changing out hardware components 1s a much more involved process 4 1 Fourier Series and the Fourier Transform The first and most important topic for discussion will be the Fourier transform The Fourier transform is related to the Fourier series which is a concept whereby any periodic signal can be represented as an infinite sum of sinusoids Each of these 17 sinusoidal components has its own frequency which is an integer multiple of the frequency of repetition in the original periodic signal The relative magnitude and phase angle of each of these sinusoids are what determine the overall shape of the original periodic signal The Single Sine form of the Fourier series is defined as 1s shown in 1 where the Co term represents the average value of the original signal the Cg and py terms are the amplitude and phase angle of each of the sinusoidal components and the w term is the radian frequency of the original periodic signal Each multiple of that f
18. er acquiring the phase response data would require more precise timing information than was available for the input and output signals A 100 mV amplitude sinusoidal signal was used as the input for this test The frequency of this signal was swept from 0 to 25 kHz again verified by the ELVIS board s oscilloscope The results of this sweep were compiled to form a magnitude 12 response plot The plotted values were normalized by the maximum recorded value They were also converted to dB for ease of reading The resulting plot is shown in Figure 4 Magnitude Response Normalized FFT Result dB No 10 10 10 10 10 10 Frequency Hz Figure 4 Magnitude Response It is clear from the plot in Figure 4 that the mic input jack acts as a band pass filter The cutoff frequencies of filters are typically defined at the 3 dB points on the magnitude response plot Using this definition this band pass filter appears to operate from roughly 7 Hz to nearly 20 kHz 3 7 Continuity Testing Once characterization of the hardware was complete the next step was to determine if the hardware would be capable of continuous recording Many recording applications require that the recording be continuous without any jumps or skips In order to test for continuity of data a sinusoidal signal was input to the mic jack In software using the PortAudio library the derivative of the collected data was calculated and recorded to a file for lat
19. er review This process was to be repeated for each buffer s worth of recorded data 13 Because the derivative of a sinusoidal signal is another sinusoidal signal the maximum value of the derivative is known If any skips in the data were to occur a discontinuity would be produced in the recorded signal which would cause the recorded derivative value to exceed its theoretical maximum Therefore any spikes in the filed derivative information would indicate a discontinuity in the recorded data Two continuity tests were conducted on the mic input jack The first was using the WMME API The input signal was a 60 Hz sinusoid with a peak to peak voltage of 0 2 V generated by the ELVIS board s FGEN The signal was sampled at 7 68 kHz so that there would be 128 samples per 60 Hz cycle The buffer was set to 1280 points This length corresponds to ten 60 Hz cycles or approximately 0 167 s The derivative was calculated from the recorded float values in real time and scaled so that the resulting sinusoid had the same amplitude as the recorded float value sinusoid The continuity test ran for 2 hours and 22 minutes before a buffer overflow error was encountered and the program stopped recording Buffer overflow is merely when the stream attempts to write new data to the application s buffer before the calculations on the old set of data have been completed This is a common problem in real time calculation systems and was caused in this case by th
20. f a Driver 4 The driver API provides a list of commands that can be accessed by programs Those commands are then translated by the API and passed to the driver kernel to execute on the sound card hardware Because of this two layer design a single driver kernel can be accessed by more than one API allowing a variety of interface configurations at the program level 2 2 PortAudio Developing the interface between an application and the driver API that is to be utilized is a non trivial task Fortunately third party libraries already exist for this purpose One such library is called PortAudio PortAudio provides a third level for interfacing with sound cards as is shown in Figure 2 2 This extra level allows the programmer to use a set of C commands to access the desired APT rather than having to conform to the specific APT commands themselves Moreover as is indicated in the diagram PortAudio is capable of interfacing with more than one API This capability allows the programmer to develop an application without knowing exactly what API 1s going to be eventually used This selection can easily be made at run time and need not be pre determined Figure 2 PortAudio and Drivers Windows APIs that are natively supported by PortAudio include Windows Multi Media Extensions WMME DirectSound and Windows Audio Session API WASAPI 2 WMME has been standard on all Windows machines since Windows 3 1 1 DirectSound is a part
21. is often dictated by the limited capabilities of the sampling hardware Digital systems contain one or more oscillators which provide electrical pulses at regular intervals This pulsing signal is often referred to as the clock signal 8 The timing of all operations in the digital system is tied inextricably to the speed of the system s oscillator No operation can occur faster than the frequency of the clock signal Also since these clock pulses serve as the triggers for commands to execute in digital systems no periodic task can operate at a frequency that 1s not a scaled version of the clock frequency For example if a given clock signal had a frequency of 1 MHz then periodic tasks could be performed at 1 MHz 500 kHz 333 33 kHz and so on Any frequency that could be found by dividing the clock frequency by an integer would be attainable However other frequencies like 800 kHz for example would not be possible using a 1 MHz oscillator Scaling a clock frequency down by dividing it by an integer is known as prescaling 9 In a real digital system the sampling frequency of an ADC must be selected from the list of available operating frequencies related to the system s oscillator Sometimes this set of available frequencies is too limiting and some method of virtually acquiring a sampling frequency outside this set is desired This process is called sample rate conversion One method of performing sample rate conversion is linear interp
22. lement these calculations using a computer to find values for a and bg they must be converted to a discrete time domain form This was accomplished by approximating the integral using trapezoidal integration to convert the integral to a sum Integration is finding the area under a curve Trapezoidal integration approximates a continuous curve from discrete points by assuming that each point is connected to the next by a straight line This straight line forms the top of a trapezoid between each pair of adjacent points The area of each trapezoid is calculated and summed to approximate the integral The resulting equations for a and bz are shown in 9 and 10 The variable M represents the total number of points in the sequence being used and f represents the fundamental frequency of the measured signal in Hertz 2 iN k Ar T f t cos wit dt 33 COS Saw km f m 1 x cos See km T 2 m 1 oe A m a me a ZY from cos FE km fim 1 cr 002 fim co Fk rim a com Gram 0 n g tn en sim a sinGrim 00 The results shown in 9 and 10 are computationally intensive For each a or by value every single point in the source sequence must be used Experimentation revealed that this level of computation could not be achieved on the test machine as a real time calculation It took longer to calculate all of the a and b values than it took to collect a buffer s worth of time domai
23. mand from the application to be read The same is true of an output stream 2 It is important to note that this stream communication method cannot guarantee continuous operation When declaring a stream using the PortAudio library an endpoint device must be selected What would normally be considered a single piece of hardware may have several endpoint devices A sound card for example may have a headphone jack and a mic jack just to name two Each of these endpoint devices is for the purposes of stream communication considered to be a completely separate device Furthermore each of these endpoint devices may be compatible with commands from more than one API In that event the PortAudio library enumerates an instance of the endpoint device for each API that could be used to communicate with it For example if the mic jack on a sound card could be controlled using either WMME or WASAPYI the PortAudio library would recognize two different mic jacks One of these jacks would be controlled using WMME and the other using WASAPI Once a PortAudio stream has been initialized communication with an endpoint device can be established It is then up to the programmer to dictate what sort of information is communicated At this point in the process the programmer can proceed with whatever processing the data requires Chapter 3 Voltage Measurement Platform Once communication has been established with a sound card device testing can begin For
24. n data This consistently led to buffer overflow errors in the program causing it to cease functioning within seconds Alternatively the a and b values could be bypassed by calculating cz directly using an FFT algorithm The Y y values could then be calculated as before and the process would then continue without disruption The new set of output variables would be identical to the previous set with a and b removed Experimentation revealed that with a buffer length of three seconds this alternative calculation method could be sustained in real time indefinitely 34 5 3 Experimental Results Once all of the real time calculations were set up an experiment demonstrating the capabilities of the measurement platform was executed The voltage at a residential 120 Vrms 60 Hz outlet was measured for a period of one week Frequency components up to the 50th harmonic were calculated All of the 3 s and 10 min values were recorded in files for later analysis Typical spectral content for the 3 s values as a percentage of the fundamental component is shown in Figure 19 Typical 10 min values are shown in Figure 20 No significant spectral content was measured beyond the 7th harmonic Smoothed 10 min values for the 3rd 5th and 7th harmonics as a percentage of the fundamental component are shown plotted over the full week in Figure 21 Typical 3s Spectrum for Yck T T T Normalized Spectral Content Typical 3s S
25. n order to ensure proper operation of a power system it is necessary to monitor the condition of that system If the system is pushed by negligence beyond what the components can handle costly damage and failure of electric service can result The condition or state of a power system refers to the voltage at every node in the system These are the basic physical quantities that are present They are complex values consisting of magnitude and phase If every complex node voltage 1s known and the impedance of every system element is known then all other quantities of interest can be found using basic circuit analysis techniques Current real power reactive power knowledge of all of these quantities is vital in maintaining a reliable power system and all of it starts with voltage When estimating the state of a power system many node voltages must be guessed The fewer guesses that have to be made the more accurate the final understanding of the state of the power system Measuring voltage is therefore an essential part of running and maintaining a reliable electric power system Many companies exist which manufacture and sell equipment for the purpose of measuring voltage These voltage measurement devices come in all shapes and sizes and are rated for many different ranges of voltage These devices will be referred to generally as data acquisition DAQ devices Modern DAQ devices commonly use analog to digital converters ADC to convert
26. nd card First it was demonstrated that the sound card is capable of continuous recording Once the appropriate API was selected for communication with the endpoint device no data was dropped or skipped The only tradeoff required to assure this continuity is to implement sample rate conversion in the application as part of data processing Second it was demonstrated that the test system was capable of performing rigorous calculations while recording data in real time Not all variables of interest could be calculated The a and b values required by the IEC standard were too computationally intensive to calculate in real time However all of the remaining values were calculated without any loss of data Finally all of the continuous recording and strenuous real time calculations were sustainable over an extended period of time As already stated the sample application experiment ran without interruption for a whole week During this time the program did not halt for any reason nor were any samples missed or calculations left incomplete 38 Now that the feasibility of this approach has been established further research 1s warranted In the harmonic measurement application used as an example in this experiment more work 1s needed to establish the frequency response of the preprocessing circuit shown in Figure 17 The assumption was made that the input impedance of the mic in port was purely resistive this is almost certainly not the case
27. ng at this 24 point that the period of this conceptual signal 1s related to the bin size of the results by 4 Because the measured samples are conceptually repeated end to end for an infinite duration it is important to make sure that there is a whole number of fundamental periods of the signal contained in a single window width If for example a sine wave with a period of 20 ms is operated on by an FFT algorithm with a window width of only 10 ms the results would not be consistent with the Fourier transform of the original continuous time domain signal In this example the window width is only half of a period Therefore the conceptual signal made up of periodically replicated sample windows contains discontinuities and clearly differs from the original continuous time signal This effect is shown in Figure 14 Original Signal Period 20 ms Conceptual Signal Window Width 10 ms 0 6 0 8 0 6 0 6 0 4 0 4 0 2 0 2 0 0 0 2 0 2 0 4 0 4 0 6 0 6 0 8 0 8 s 0 10 20 30 40 50 60 7 0 10 20 30 40 50 60 Time ms Time ms Figure 14 Signal Window Periodicity Example 4 3 Sample Rate Conversion The sampling frequency used to acquire a discrete time domain signal from a continuous time domain signal affects both frequency bleeding and aliasing and is further limited by the need to have a power of two number of samples per window width This 29 frequency therefore must be chosen with care However sampling frequency
28. nsidered the reference value or ground The range of values available to the 32 bit floating point format is 1 0 to 1 0 2 In a PortAudio stream the buffer length parameter determines how many data points are passed to or from the hardware at a time This value can be automatically assigned by the PortAudio library to optimize performance However if the buffer length is automatically assigned the length may vary over time In the event that an application requires a specific buffer length the length can be specified to be any arbitrary integer value 2 There are two methods of communication between a stream and an application The first method is by way of a callback function This method raises an interrupt every time the streams buffer fills for input or empties for output A developer defined function is then run to collect and pass on whatever information is necessary This function operates at a high priority and must resolve as quickly as possible in order to avoid interfering with other operations Therefore the callback function 1s prohibited from containing any memory allocation or file writing instructions Failure to abide by this rule can lead to runtime errors 2 The second stream communication method provided by the PortAudio library 1s a blocking scheme This method entrusts the timing of communication to the application rather than to interrupts This means that an input stream buffer will fill and then wait for a com
29. olation This method functions by approximating the original continuous time domain signal by connecting all of the samples in the discrete time signal by straight lines Once the original signal is approximated new points are sampled in software virtually 26 approximating any desired sampling frequency An example of this process is shown in Figure 15 50 Hz Sine Wave Sampled at 500 Hz T T sin 2x1rx50xt b 0 5 10 15 20 Time ms Signal Reconstructed from Samples Reconstructed Signal Virtually Sampled at 200 Hz T T T T sin 2x1rx50xt sin 2x1rx50xt x x 1 1 0 5 10 15 20 0 5 10 15 20 Time ms Time ms Figure 15 Sample Rate Conversion by Linear Interpolation This approach does have limitations The primary limitation 1s that the reconstructed version of the original signal is not perfect Because of this some error 1s introduced into the new virtually sampled sequence In order to limit the effects of this error the original sampling frequency should be greater than the virtual sampling frequency that is desired which in turn should be at least as fast as the Nyquist rate 27 Chapter 5 Sample Application Now that the necessary concepts of signal processing are understood it is possible to proceed with implementing a harmonic measurement scheme using a PC sound card as a voltage measurement device Harmonic measurement is a broad catego
30. ontinuous time domain signal This operation is accomplished through the use of an ADC In the specific case of the PC sound card measurement platform this operation is performed by the sound card hardware in concert with the driver software Additionally any sample rate conversion that is required is performed in the sampling step Because an FFT routine is used in later steps it is important to collect a power of two number of samples in every sample window The IEC standard dictates that the window width be 200 ms 10 This length of time corresponds to ten cycles in a 50 Hz power system and twelve cycles in a 60 Hz power system As such a virtual sampling rate of 10 24 kHz was selected to produce 2048 samples in every 200 ms window Assuming that the highest frequency of interest in the recorded signals is the 50th harmonic of a 60 Hz power system 3 kHz the Nyquist rate for this measurement setup is 6 kHz The selected virtual sampling rate is faster than the 30 Nyquist rate and is slower than the hardware sampling rate and should therefore result in minimal error The DFT block performs the discrete time Fourier transform on the sampled sequence The frequency domain results are referred to as Output 1 and are passed to the next block for further processing The individual quantities that are calculated to form Output 1 are az by and Y p The first two quantities are the coefficients in the sine cosine form of the Fourier series
31. p the recorded values back to the outlet voltage This mapping requires some calibration in the program In this case the calibration was performed using circuit analysis based on the circuit values shown in Figure 17 and the transfer characteristics shown in Figure 3 Smoothed Fundamental Component T T T T 125 124 123 f 122 Voltage Wrms 121 120 119 118 0 Time days Figure 22 Recorded 60 Hz Voltage At a later time than when the experiment was run independent measurements were taken of the same outlet voltage using a DMM These measurements were taken periodically over several hours and ranged from 120 9 Vrms to 123 0 Vrms These values seem to corroborate the values shown in Figure 22 However without extensive testing it is impossible to verify that the harmonic measurement results are accurate No claim 1s being made to that effect Instead these results clearly demonstrate that this design for a voltage measurement platform using a PC sound card 1s capable of meeting all usability requirements oy Chapter 6 Conclusions The program written as the core of this project was able to communicate with and help quantify the electrical characteristics of an example PC sound card Use of the PortAudio library allowed for a simple interface between C code and the sound card hardware regardless of driver specifics Overall the usability requirements as set out in the Introduction were met by the tested sou
32. pectrum for Ygh Typical 3s Spectrum for Yogh T T T T T T Normalized Harmonic Content 9 Normalized Harmonic Content 9 r 9 9 9 9 2 3 4 5 6 7 8 2 3 4 5 6 Harmonic Order x 60 for Hz Harmonic Order x 60 for Hz S o oo le Figure 19 Typical Three Second Spectra 35 Normalized Harmonic Voltage Normalized Harmonic Content 14 1 0 8 0 6 04 0 2 1 6 1 25 0 8 F 04 0 Typical 10min Spectrum for Yck Normalized Spectral Content Harmonic Order x 60 for Hz Typical 10min Spectrum for Ygh Typical 10min Spectrum for Yogh 14 1 2 0 8 0 6 04 Normalized Harmonic Content 0 2 4 5 6 7 8 2 3 4 5 6 7 8 Harmonic Order x 60 for Hz Harmonic Order x 60 for Hz Figure 20 Typical Ten Minute Spectra Smoothed 3rd Harmonic 14 T T L s T E w T ho T 15 0 9 T Normalized Harmonic Voltage se co T 1 L l 1 1 2 3 4 5 6 7 Time days e J a E Smoothed 5th Harmonic Smoothed 7th Harmonic 1 3 T E T Y T TE TZE LAF Normalized Harmonic Voltage 09t 0 8f 0 7 P OGF 05 L L l L L 1 3 4 5 6 7 0 1 2 3 4 5 6 7 Time days Time days Figure 21 Smoothed Values for 3rd 5th and 7th Harmonics 36 The plots in Figures 19 through 21 are scaled based on the recorded value for the fundamental component However the time domain plot in Figure 22 attempts to ma
33. performed on the virtually sampled signal Also the buffer 15 was extended to accommodate one second of data in order to eliminate the buffer overflow issue This second continuity test ran for 8 hours and 24 minutes It was ended voluntarily without encountering any errors Upon examination of the recorded derivative data file no spikes were found meaning that there were no skipped samples for the entire duration of the experiment This result clearly indicates the superiority of accessing hardware through WASAPI over WMME Since WASAPI does not perform any sample rate conversion the latency of the recording operation is relatively low and no samples are skipped The assurance of continuity using WASAPI does come at a price however Every buffer s worth of data must be interpolated to the appropriate sampling frequency by the application This extra action uses valuable processing time before the next buffer s worth of data is ready for processing 16 Chapter 4 Signal Processing Principles Once all of the necessary characteristics have been established the sound card is ready for use as a voltage measurement platform However in order to demonstrate the capabilities of this measurement device an example application has been selected The application that will be explored is that of harmonic measurement of voltage in the power system As 1s implied by the name harmonic measurements deal with signals containing multiple frequ
34. requency is called a harmonic 5 Alternatively the Fourier series can be expressed in a sine cosine form as shown in 2 f t co Cg Sin kw t og 1 k 1 f t ao gt ag cos kw t by sin kw t 2 k 1 The series shown in 1 relates amplitudes and angles to specific frequencies The Fourier transform can be used to find these quantities This transform converts a continuous time domain signal into a continuous frequency domain signal Example signals before and after applying the Fourier transform are shown in Figure 6 From this result the harmonic information shown in 1 can be acquired 18 Fourier Transform Input Fourier Transform Results 3 6 Ha 3f 0 6 25 0 5 FTE tt in x Time ms Frequency kHz Figure 6 Fourier Transform Example The Fourier transform holds for continuous time signals However in the digital domain all signals are discrete time For such signals the discrete time Fourier transform DTFT must be used The DTFT takes a discrete time domain signal and generates a continuous frequency domain signal As is shown in Figure 7 the results of the DTFT are periodic whereas the results of the Fourier transform are not This fact leads to the potential for aliasing which will be discussed later DTFT Output DTFT Input 0 7 o o y om Sa t IDTFT x n x 0 2 0 1 0 30 20 10 0 10 20 30 Frequency kHz Figure 7 DTFT Example The DTFT can
35. ry which encompasses everything to do with measuring and calculating quantities related to harmonic components present in power signals In relation to topics such as this one it 1s important to carefully define what is measured and how it is calculated One source of these definitions can be found in IEC standard number 61000 4 7 10 This standard clearly lays out what exactly is meant by harmonic measurement 5 1 IEC 61000 4 7 The IEC definition of harmonic measurement applies to measuring voltage quantities and is therefore applicable to the PC sound card measurement platform The harmonic measurement process according to the IEC standard 10 1s shown in Figure 16 The preprocessing block refers to any operations that must be performed on the continuous time domain signal before sampling Anti aliasing is an example of an operation that would occur in this step However designing and building an analog low pass filter was deemed outside the scope of this project and therefore will not be discussed 28 Input Voltage Output 1 Output 2a Output 2b Figure 16 Harmonic Measurement Process Another issue that would be handled in preprocessing is that the voltage signal that is to be measured for this example application is a 120 Vrms signal from a residential outlet Because the maximum input amplitude of the mic input jack was determined to be 130 mV some preprocessing of the signal 1s necessary to reduce the voltage to an accep
36. table level The circuit used for this preprocessing 1s shown in Figure 17 33 9 kOhm Ro es tke Rin 120 Vms DAO KOhM e ee 2 56 kOhm Figure 17 Preprocessing Circuit Diagram The first step in reducing the input voltage was to connect a transformer The transformer that was used was a PARALINE 55C5 4 480 Though the rated turns ratio was 120 1 experimentation revealed that the effective turns ratio was closer to 106 1 The transformer drops the input voltage to approximately 1 Vrms Clearly this is still too high to be used as input to the mic jack Therefore a voltage divider network was used to reduce the voltage a little further Resistors R1 and R2 in Figure 17 make up this network 29 Finally the input resistance of the mic jack was measured using a digital multi meter DMM while the device was recording This measured value is shown as Rin in Figure 17 This approximate model of the preprocessing circuit leads to calculating an input voltage of approximately 54 mV peak for a supply voltage of 120 Vrms This value is below the maximum recordable voltage for the mic input jack of 130 mV peak Furthermore using the previously established conversion chart from input voltage to recorded floating point value along with the transformer and voltage divider network 120 Vrms roughly maps to a peak float value of 0 399 The sampling block refers to the process of creating a discrete time domain signal from the preprocessed c
37. tada 19 DERE molins cua a tne 20 Fourier Transform Frequency Envelope ooooooccccccccoccccnnnccconononoos 23 Transformed Signal Sampled at the Nyquist Rate 0oooooococcco 23 Transformed Signal Sampled at Below the Nyquist Rate 23 Low pass Filtered Signal Spectrum 0 cece cece cece eee eeee eee eeeees 24 SUCCESSIULAMU AMASING reina 24 Signal Window Periodicity Example ccccccee eee e eee e cece cece een e 29 Sample Rate Conversion by Linear Interpolati0N o00oooooocoooommoo 27 Harmonie Meas rement Procesan 29 Preprocessine Circuit Did Stains AA AAA A 29 Smoothing Filter Dia eran ici ada isla 32 Typical Three second PEA 35 yi Figure 20 Typical Ten Minute Spectra 00 cece a a Figure 21 Smoothed Values for 3rd 5th and 7th Harmonics cceeeee eee Figure 22 Recorded OOFZ Volar uscar ds Vil List of Abbreviations ADC Analog to Digital Converter API Application Programming Interface DAQ Data Acquisition DFT Discrete Fourier Transform DMM Digital Multi Meter DTFT Discrete Time Foutier Transform FFT Fast Fourier Transform FGEN Function Generator WASAPI Windows Audio Session API WMME Windows Multi Media Extensions Vill Chapter 1 Introduction Electric power is central to modern culture and industry Ensuring that electrical power 1s provided in a reliable fashion is therefore of the utmost importance I
38. us time domain signal must be processed with a low pass filter to remove any frequency components that are above the maximum allowed frequency for a given sampling rate This process 1s called anti aliasing 7 Itis important to note that since aliasing occurs at the time of sampling this filtering must occur in the continuous time domain for maximum effect 23 If x t were to be passed through an anti aliasing filter the maximum frequency of the result y t would now be the cutoff frequency of the filter A representation of the resulting signal spectrum 1s shown in Figure 12 Because the maximum frequency content of the signal has been lowered the Nyquist rate for the signal 1s also lowered Correct selection of f can eliminate aliasing altogether This scenario is represented in Figure 13 FT y t Figure 13 Successful Anti Aliasing The final issue of concern with regards to the FFT operation is signal window periodicity The DFT and therefore the FFT take a finite number of points as time domain input However the concept that the FFT is built on requires the time domain signal to be periodic with infinite duration This is dealt with mathematically by making the assumption that the window in the time domain signal is repeated to infinite time In this way the signal is made to be in concept a periodic signal with infinite duration 7 The period of this conceptual signal is the window width Ty It is worth noti
39. used for this experiment was an NI ELVIS II prototyping board This device houses among other things a digital function generator According to the user s manual for the ELVIS board 4 the ELVIS board s function generator FGEN is capable of supplying a sinusoidal signal with peak to peak amplitude of up to 10 V and a frequency of up to 50 MHz decimated by a 28 bit frequency divider for a frequency step of 0 18626 Hz This theoretical step size was validated by observation The frequency of the output signal varied by no more than 0 1 Hz at any point during experimentation 3 3 PortAudio Choices Once a signal generator was acquired the next step was to set up a recording program The mic input jack provides two input channels that the PortAudio library can access For the purposes of this experiment only one of these channels was used The data format selected for recording by the PortAudio library was 32 bit floating point As mentioned previously this data format has a maximum value of 1 0 and a minimum value of 1 0 The mic input jack is capable of receiving commands through more than one API Two of the APIs that could access this endpoint device were WMME and WASAPI Consequently the PortAudio library enumerated two separate mic input jacks one through WMME and the other through WASAPI 10 3 4 Sampling Rate Capabilities Both mic input jack endpoint devices were tested for the range of available sampling frequencies
40. using the built in functions of the PortAudio library The endpoint devices were selected by input streams and then tested with multiple sampling frequencies until the full range for each was found The full range of available sampling frequencies for the WMME API was found to be kHz to 200 kHz On the other hand WASAPI provided 44 1 kHz as the only available sampling frequency A device s list of available sampling frequencies is limited by the device s clock frequency Therefore the lists of available sampling frequencies for both WMME and WASAPI indicate that WMME automatically performs sample rate conversion and WASAPI does not This supposition was supported by literature review 3 Furthermore this result also indicates that the oscillator on board the soundcard operates at an integer multiple of 44 1 kHz 3 5 Transfer Curve In order to find an input voltage to output 32 bit floating point number mapping curve the ELVIS board s FGEN was used to generate a sinusoidal signal with a frequency of 60 Hz This frequency was chosen because it is a frequency of primary interest in power system measurements The amplitude of the input sinusoid was swept and the results are shown in Figure 3 The amplitude and frequency of the FGEN output was verified using an oscilloscope also housed on the ELVIS board These results clearly indicate a linear relationship between input and output with maximum meaningful input 11 voltage amplitude of
Download Pdf Manuals
Related Search